We now apply this energy-preserving piDMD to study the flow
past a cylinder, which is a benchmark problem for modal decompositions [1]}.
The Reynolds number is \(Re = D U/\nu = 100\) 
where \(D\)  is the diameter of the cylinder, \(U\)  is the free-stream velocity and \(\nu \) 
is the kinematic viscosity.
The data consist of 151 samples of vorticity measurements, corresponding to five periods of vortex shedding, taken on a grid of 199\(\times \) 449 points.
We note that the 2-norm of the measurements is approximately constant in time.
The data are contaminated with 20% Gaussian noise, as illustrated in the
top left panel of figure REF .
We truncate the data to the first 15 POD modes and learn a standard DMD model,
and an energy-preserving piDMD model.
